Since manipulatives are restricted to geometrical objects, their exploratory character is limited compared to explorations, which provide a far richer context for inducing and practicing more sophisticated mathematical ideas, for instance, the concept of rate of change.
Exploratory computerized environments (ECEs), focusing on supporting mathematical explorations and problem solving, share many commonalities with scientific discovery.
Moreover, we introduce the landmark-based guided graph exploration and probe-based graph exploration which requires much less space overhead.
This way exploration stays "near the path" which leads to faster convergence than random exploration, which we had also tried but abandoned for this reason.
A graduate of the élite École Normale Supérieure, he had recently completed his doctorate, a dense mathematical exploration of the theory behind tax policies.
The award of the Fields Medal to Manjul Bhagarva is notable not only because he plays the tabla drum professionally in his spare time but also because of his novel use of computers in mathematical exploration.
However, taken by itself a definition need not be a specification of anything; it may just form part of a mathematical exploration.
It is observed that this formalism brings an ease in further mathematical exploration and also helps to understand the geometric properties of such operators better.
Nevertheless, the mathematical exploration of chaos in dynamical systems helps us to understand some of the pitfalls that may attend our efforts to know whether our world is genuinely deterministic or not.
Creating an atmosphere of engaging mathematical exploration for thousands of students has not been easy - it requires much more preparation of teachers.
